Spatiotemporal bounded noises and transitions induced by them in solutions of the real Ginzburg-Landau model

In this work, we introduce two spatiotemporal colored bounded noises, based on the zero-dimensional Cai-Lin and Tsallis-Borland noises. Then we study and characterize the dependence of the defined stochastic processes on both a temporal correlation parameter τ and a spatial coupling parameter λ. In particular, we found that varying λ may induce a transition of the distribution of the noise from bimodality to unimodality. With the aim of investigating the role played by bounded noises in nonlinear dynamical systems, we analyze the behavior of the real Ginzburg-Landau time-varying model additively perturbed by such noises. The observed phase transition phenomenology is quite different from that observed when the perturbations are unbounded. In particular, we observed an inverse order-to-disorder transition and a reentrant transition, with dependence on the specific type of bounded noise.